The linearized semiclassical initial value representation ~LSC-IVR! @H. Wang, X. Sun and W. H. Miller, J. Chem. Phys. 108, 9726 ~1998!# is used to study the nonadiabatic dynamics of the spin-boson problem, a system of two electronic states linearly coupled to an infinite bath of harmonic oscillators. The spectral density of the bath is chosen to be of the Debye form, which is often used to model the solution environment of a charge transfer reaction. The simulation provides a rather complete understanding of the electronically nonadiabatic dynamics in a broad parameter space, including coherent to incoherent transitions along all three axes ~the T-axis, the h-axis, and the vc-axis! in the complete phase diagram and the determination of rate constants in several physically interesting regimes. Approximate analytic theories are used to compare with the simulation results, and good agreement is found in the appropriate physical limits.